4 Oligopoly and Strategic Competition

Oligopoly and interdependence

An oligopoly is a market dominated by a small number of firms. Entry barriers—including large economies of scale, patents, or established brands—can help preserve this market structure.

Because each firm is large enough to affect market outcomes, its decisions about price, output, advertising, or investment depend in part on what rivals do. This mutual dependence is strategic interdependence.

Strategic choices and the prisoner’s dilemma

Game theory analyzes strategic choices by specifying the players, their available strategies, and the payoffs each receives for each resulting combination of choices. A strategy is a best response when it gives a player the highest payoff given the other players’ strategies. A Nash equilibrium is a set of strategies in which every player is choosing a best response to the others; no player can gain by changing strategy alone. A dominant strategy is a best choice regardless of what the other player does.

A two-firm output game

Suppose two firms can either hold output down or expand it. Payoffs are profits, with Firm A’s amount listed first:

• Both hold output down: Firm A earns $\$1{,}000$, and Firm B earns $\$1{,}000$.

• Firm A holds output down and Firm B expands: Firm A earns $\$200$, and Firm B earns $\$1{,}500$.

• Firm A expands and Firm B holds output down: Firm A earns $\$1{,}500$, and Firm B earns $\$200$.

• Both expand: each earns $\$400$.

For either firm, expanding is the dominant strategy: it earns more whether the rival holds output down or expands. The resulting outcome is that both expand and earn $\$400$ each, even though both would earn more if they could reliably hold output down together. This conflict between individually tempting choices and a better joint outcome is a prisoner’s dilemma. It helps explain why firms may compete aggressively even when cooperation would raise combined profits.

Repeated interaction and cooperation

When firms interact repeatedly, expected future rewards or retaliation can change their incentives. For example, a firm might refrain from undercutting a rival if it expects that rival to respond in future periods.

Whether cooperation can be sustained depends on how often firms interact, how quickly they can detect deviations, and how much they value future profits.

Quantity and price competition

Oligopoly models differ in what firms choose and when they choose it. Their assumptions matter, so no single outcome describes every oligopoly.

Cournot: simultaneous quantity choices

In the Cournot model, firms choose quantities simultaneously, treating rivals’ quantities as given when selecting their own. The market price depends on total output. Each firm has a reaction function: its best-response quantity for each possible quantity produced by its rivals. A Cournot equilibrium occurs where firms’ choices are mutual best responses.

For two identical firms facing inverse demand $P=a-bQ$, where $Q=q_1+q_2$, and constant marginal cost $c<a$, the equilibrium quantities are

Each firm accounts for the effect of its own output on the market price, but not the full effect of additional industry output on its rival. Compared with a monopoly, firms typically produce more in total and charge a lower price. With more identical firms, the standard Cournot outcome moves toward the competitive outcome.

Bertrand: simultaneous price choices

In the Bertrand model, firms choose prices simultaneously. With a homogeneous product, identical constant marginal costs, and no capacity constraints, each firm can attract customers by slightly undercutting a rival’s price. In the standard model, this pressure drives equilibrium price to marginal cost, even with just two firms.

This sharp result depends on its assumptions. Product differentiation, capacity limits, or cost differences can soften price competition and allow prices above marginal cost. With differentiated products, each firm’s demand depends on its own price and on rivals’ prices, so firms may retain some market power.

Stackelberg: sequential quantity choices

In the Stackelberg model, firms compete in quantities, but one firm chooses first and the other observes that choice before responding. The first mover is the leader, and the responding firm is the follower. The leader anticipates the follower’s reaction and chooses output accordingly.

With two identical firms, linear inverse demand $P=a-bQ$, and constant marginal cost $c$, the standard model gives the leader output $\frac{a-c}{2b}$ and follower output $\frac{a-c}{4b}$. The leader’s commitment to a relatively large output can therefore give it a first-mover advantage in this model.

Collusion and kinked demand

Firms that coordinate output or prices to raise joint profits are colluding; a formal agreement to do so is a cartel. Coordination can make the market outcome resemble monopoly, but each firm may gain by secretly expanding output or cutting price. This incentive to deviate makes cooperation difficult to maintain.

The kinked-demand model offers one proposed explanation for why an oligopolist might be reluctant to change its price. It assumes rivals match price cuts but do not match price increases. A price cut then brings little extra business, while a price increase risks losing many customers. The firm’s perceived demand curve has a kink at the prevailing price, and the corresponding gap in marginal revenue can make price relatively unresponsive to moderate cost changes. This is a proposed explanation, not a universal account of oligopoly pricing.

Choosing a model

The models differ in firms’ choices, decision timing, and the assumptions used to describe rivalry:

• Cournot: Firms choose quantities simultaneously; in the standard version, their output choices are mutual best responses.

• Bertrand: Firms choose prices simultaneously; under the standard assumptions for identical goods, undercutting can drive price to marginal cost.

• Stackelberg: Firms choose quantities sequentially; a leader anticipates the follower’s response.

• Kinked demand: Firms choose prices while considering rivals’ reactions; asymmetric responses can make price changes unattractive. It is not specified by a single strategic game.

These are simplified frameworks, not universal descriptions. To apply one, identify the product, the firms’ strategic choices, the timing of decisions, and the assumptions about costs, capacity, and rivals’ reactions.